Zentralblatt MATH

Publications of (and about) Paul Erdös

Zbl.No: 709.11015
Autor: Erdös, Paul; Maxsein, Th.; Smith, P.R.
Title: Primzahlpotenzen in rekurrenten Folgen. (Prime powers in recurrent sequences.) (In German)
Source: Analysis 10, No.1, 71-83 (1990).
Review: Authors' abstract: We determine the structure of recurrent sequences of natural numbers which consist only of primes or prime powers. For example it is shown that a recurrent sequence of primes must be periodic. In order to obtain the results, the theorem of Mahler-Lech is used to bound the number of distinct infinite multiplicity values taken by a recurrent sequence of complex numbers. Further we employ a theorem of Pólya about recurrent sequences (an) of integers such that the set of primes p, for which p|an for some n, is finite.
Reviewer: P.Kiss
Classif.: * 11B37 Recurrences 30B40 Analytic continuation (one complex variable)
Keywords: power series; recurrent sequences; primes; prime powers